find f(x) and simplify.\nf(x)=\frac{x}{x + 50}\nwhich of the following shows the correct application of the…

find f(x) and simplify.\nf(x)=\frac{x}{x + 50}\nwhich of the following shows the correct application of the quotient rule?\na. \frac{(x + 50)(1)-(x)(1)}{x + 50^2}\nb. \frac{(x)(1)-(x + 50)(1)}{x^2}\nc. \frac{(x)(1)-(x + 50)(1)}{x + 50^2}\nd. \frac{(x + 50)(1)-(x)(1)}{x^2}

find f(x) and simplify.\nf(x)=\frac{x}{x + 50}\nwhich of the following shows the correct application of the quotient rule?\na. \frac{(x + 50)(1)-(x)(1)}{x + 50^2}\nb. \frac{(x)(1)-(x + 50)(1)}{x^2}\nc. \frac{(x)(1)-(x + 50)(1)}{x + 50^2}\nd. \frac{(x + 50)(1)-(x)(1)}{x^2}

Answer

Explanation:

Step1: Recall quotient - rule

The quotient - rule for a function $y=\frac{u(x)}{v(x)}$ is $y^\prime=\frac{v(x)u^\prime(x)-u(x)v^\prime(x)}{[v(x)]^2}$. For $f(x)=\frac{x}{x + 50}$, let $u(x)=x$ and $v(x)=x + 50$.

Step2: Find $u^\prime(x)$ and $v^\prime(x)$

If $u(x)=x$, then $u^\prime(x)=1$. If $v(x)=x + 50$, then $v^\prime(x)=1$.

Step3: Apply quotient - rule

Substitute $u(x),v(x),u^\prime(x),v^\prime(x)$ into the quotient - rule formula: $f^\prime(x)=\frac{(x + 50)(1)-(x)(1)}{(x + 50)^2}$.

Answer:

A. $\frac{(x + 50)(1)-(x)(1)}{(x + 50)^2}$